Chakra Veerakul
Yes :)
There are many types of peace and happiness I believe. The obvious one is when meditation makes us rest in the present moment, fully aware of ourselves and people around us. This means that we are not looping emotions, dwelling in the past, or dreaming of the future. We understand that it is illogical to do so.
For example, when someone offends us, we get angry and may offend them back. With our minds focused on the present moment, we would realize many truths about anger. Ex.
"Anger does no good to no one", or "who we are is not related with what others say about us, so why so angry?" Or "insults end when the person finished insulting, it is our minds that make them last."
Yet, there is a deeper state of peace. From my understanding of Buddhism and Psychology, our perceptions notice that matters have different shapes, textures, sounds, odors and tastes; therefore, we subconsciously believe that they are different. In fact, it is our perceptions that differentiate them.
Using the same example (when someone offends us), we'd notice that our minds create illusions that ourselves exist, that the offender exists and that the offensive words have meanings. Then the defensive mechanism kicks in and we feel hurtful of being offended and want to offend the offender back.
With minds well-trained in meditation (having the ability to focus), we are able to maintain the realization of the truth: the sameness of things. In other words, recode the subconscious mind to its original state. Then, the mind rests in an indifferent state, which is the enlightenment. This is quite different from ordinary happiness, since it is an ego-less one.